A244940 T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than sqrt(3) standard deviations from its mean

2, 3, 4, 4, 9, 8, 5, 14, 25, 14, 6, 23, 52, 69, 28, 7, 34, 111, 198, 207, 56, 8, 43, 190, 517, 764, 603, 104, 9, 58, 295, 1076, 2529, 2976, 1741, 208, 10, 75, 444, 1939, 6370, 12497, 11668, 5223, 416, 11, 94, 631, 3358, 13139, 37364, 60773, 45960, 15445, 796, 12, 109

Offset

1,1

Comments

Table starts

...2.....3......4.......5........6.........7.........8..........9.........10

...4.....9.....14......23.......34........43........58.........75.........94

...8....25.....52.....111......190.......295.......444........631........896

..14....69....198.....517.....1076......1939......3358.......5405.......8450

..28...207....764....2529.....6370.....13139.....26256......47837......81956

..56...603...2976...12497....37364.....89937....203496.....414005.....802938

.104..1741..11668...60773...219382....619567...1606524....3633503....7812680

.208..5223..45960..293467..1290578...4214681..12610616...32062641...76978472

.416.15445.181652.1452027..7608118..29077603..98974880..284037099..754859772

.796.45423.719784.7098491.44939408.198628937.777361848.2523617923.7399299882

Computation in integer form, using 6 times the 0..k mean and 36 times the variance, mean6(k)=3*k; var36(k)=6*k*(2*k+1)-mean6(k)^2; then (6*sum{x(i),i=1..j}-j*mean6(k))^2<=3*j*var36(k) for all j=1..n

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Example

Some solutions for n=6 k=4
..4....1....2....0....4....3....3....0....1....1....3....1....0....4....3....4
..1....3....1....4....0....0....1....3....3....0....4....4....4....1....3....1
..3....1....0....2....4....4....4....2....3....3....3....0....2....2....0....1
..3....3....4....3....3....2....4....1....1....2....2....4....4....1....3....4
..4....1....1....2....3....4....0....1....1....2....3....4....3....0....0....0
..3....3....0....4....3....3....0....0....1....3....0....4....2....1....3....4

Crossrefs

Row 1 is A000027(n+1)

Sequence in context: A228461 A267471 A268457 * A244832 A250351 A269690

Adjacent sequences: A244937 A244938 A244939 * A244941 A244942 A244943

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 08 2014

Status

approved